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Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization

2020-01-01Artigo científico Acesso aberto
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dc.contributor.authorBrás, C. P.
dc.contributor.authorMartínez, José Mário
dc.contributor.authorRaydan, M.
dc.contributor.institutionCMA - Centro de Matemática e Aplicações
dc.contributor.institutionDM - Departamento de Matemática
dc.contributor.pblSpringer Science Business Media
dc.date.accessioned2020-05-14T22:58:07Z
dc.date.available2022-03-09T01:31:27Z
dc.date.embargoedUntil2020-10-19
dc.date.issued2020-01-01
dc.descriptionPRONEX-CNPq/FAPERJ (E-26/111.449/2010-APQ1), CEPID-Industrial Mathematics/FAPESP (Grant 2011/51305-02), FAPESP (Projects 2013/05475-7 and 2013/07375-0). Fundacao para a Ciencia e a Tecnologia- project UID/MAT/00297/2019 (CMA).
dc.description.abstractWe present a new algorithm for solving large-scale unconstrained optimization problems that uses cubic models, matrix-free subspace minimization, and secant-type parameters for defining the cubic terms. We also propose and analyze a specialized trust-region strategy to minimize the cubic model on a properly chosen low-dimensional subspace, which is built at each iteration using the Lanczos process. For the convergence analysis we present, as a general framework, a model trust-region subspace algorithm with variable metric and we establish asymptotic as well as complexity convergence results. Preliminary numerical results, on some test functions and also on the well-known disk packing problem, are presented to illustrate the performance of the proposed scheme when solving large-scale problems.en
dc.description.versionauthorsversion
dc.description.versionpublished
dc.format.extent596238
dc.identifier.doi10.1007/s10589-019-00138-1
dc.identifier.issn0926-6003
dc.identifier.otherPURE: 15494912
dc.identifier.otherPURE UUID: 3479327b-691a-4fa6-833f-43f539ba05bc
dc.identifier.otherScopus: 85074596050
dc.identifier.otherWOS: 000490886300001
dc.identifier.urihttp://hdl.handle.net/10362/97712
dc.identifier.urlhttps://www.scopus.com/pages/publications/85074596050
dc.language.isoeng
dc.peerreviewedyes
dc.subjectCubic modeling
dc.subjectDisk packing problem
dc.subjectLanczos method
dc.subjectNewton-type methods
dc.subjectSmooth unconstrained minimization
dc.subjectSubspace minimization
dc.subjectTrust-region strategies
dc.subjectControl and Optimization
dc.subjectComputational Mathematics
dc.subjectApplied Mathematics
dc.titleLarge-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimizationen
dc.typejournal article
degois.publication.issue1
degois.publication.titleComputational Optimization And Applications
degois.publication.volume75
dspace.entity.typePublication
rcaap.rightsopenAccess

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